These are rank three temperaments tempering out 540/539, but we can began by looking at the rank four temperament.

Comma: 540/539

Map: [<1 0 0 0 2|, <0 1 0 0 3|, <0 0 0 1 -2|]
Generators: 2, 3, 5, 7
EDOs: 9, 10, 19, 22, 31, 41, 53, 58, 72, 130, 152, 224, 354, 537, 578

Hades

Commas: 540/539, 4000/3993

Map: [<2 1 0 2 3|, <0 3 0 5 -1|, <0 0 1 0 1|]
Generators: 99/70, 9/7, 5
EDOs: 22, 50, 58, 72, 130, 152, 224, 354, 578
Badness: 0.000361

13-limit

Commas: 540/539, 729/728, 1575/1573

Map: [<2 1 0 2 3 -2 |, <0 3 0 5 -1 13|, <0 0 1 0 1 0|]
Generators: 99/70, 9/7, 5
EDOs: 36, 58, 72, 130, 224, 354, 578
Badness: 0.000535

Cerberus

Commas: 351/350, 364/363, 540/539

Map: [<2 1 0 2 3 1|, <0 3 0 5 -1 -4|, <0 0 1 0 1 2|]
Generators: 55/39.9/7.5
EDOs: 22, 50, 58, 72, 130
Badness: 0.000766

Minos

Commas: 540/539, 12005/11979

Map: [<1 0 2 1 2|, <0 2 4 3 4|, <0 0 -5 -1 -3|]
Generators: 2.121/70.49/33
EDOs: 9, 49, 58, 72, 130, 193, 202, 467
Badness: 0.000886

13-limit

Commas: 364/363, 540/539, 676/675

Map: [<1 0 2 1 2 1|, <0 2 4 3 4 7|, <0 0 -5 -1 -3 -5|]
Generators: 2.26/15.49/33
EDOs: 9, 54, 58, 72, 121, 130, 193
Badness: 0.000724

Persephone

Commas: 540/539, 88209/87500

Map: [<1 0 4 -2 10|, <0 1 4 0 7|, <0 0 -5 3 -11|]
EDOs: 50, 53, 58, 103, 108, 111, 161, 214, 272, 375, 1022bcde, 1236bcde, 1397bcde
Badness: 0.002015

13-limit

Commas: 351/350, 540/539, 847/845

Map: [<1 0 4 -2 10 7|, <0 1 4 0 7 5|, <0 0 -5 3 -11 -7|]
EDOs: 50, 53, 58, 103, 108, 111, 161, 214, 375, 700cdef, 861bcdef, 1075bcdef, 1236bcdef, 1450bcdef
Badness: 0.000997

Hypnos

Commas: 540/539, 72171/71680

Map: [<1 0 0 -3 8|, <0 3 0 11 -13|, <0 0 1 0 1|]
EDOs: 19, 36, 53, 72, 161, 197e, 214, 233, 286, 358, 591be, 663be, 949bce
Badness: 0.001629

13-limit

Commas: 169/168, 540/539, 729/728

Map: [<1 0 0 -3 8 0|, <0 3 0 11 -13 7|, <0 0 1 0 1 0|]
EDOs: 19, 36, 53, 72, 125f, 197ef
Badness: 0.001439